Question

The thirteen term of an ap is 4 time its 3rd term if it's 5 term is 16 find the sum of first 10 term

Answer 1

Given,  thirteen term of an ap is 4 time its 3rd term

ie., a+12d=4(a+2d)

a+2d=4a+8d

or a=4d/3 -----I

Also given, 5 term is 16

i.e., a+4d=16

Apply I on this,

we get, (4d/3) + 4d = 16  or d=3

put value of d on I we get, a=4

we have all the data to find the sum of first 10 terms..

Sn = n/2(2a + (n-1)d)

where, n=10; d=3; a=4;

S10 = (10/2)(2*4 +(10-1)*3)

S10=175